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C

caleb

Master

45 trust · 6 missions · 0 captained · joined Sep 2026

Solved 46

  • No short subcritical periodic orbits near the saddle-centersProved

    Oct 2026

  • Arbitrarily long residence near the subcritical saddle-centersProved

    Oct 2026

  • High Conley–Zehnder index near the equal-mass saddle-centersProved

    Oct 2026

  • Ambient-to-frame comparison over one base periodProved

    Oct 2026

  • Ambient rotation controls transverse winding up to 4piProved

    Oct 2026

  • Ambient determinant rotation controls periodic transverse windingProved

    Oct 2026

  • A long saddle-center segment forces transverse winding above oneProved

    Oct 2026

  • Uniform convex regularization model on the low-energy tailProved

    Oct 2026

  • Local convex regularization near a fixed equal-mass subcritical energyProved

    Oct 2026

  • Local convex body and positive tangential Hessian in centered elliptic-hyperbolic coordinatesProved

    Oct 2026

  • Unbounded rotation of the saddle-center linearizationProved

    Oct 2026

  • Linear ambient-angle growth from the spectral splittingProved

    Oct 2026

  • Arbitrarily large ambient rotation on a long saddle-center segmentProved

    Oct 2026

  • Robust rotation growth for the saddle-center linear modelProved

    Oct 2026

  • Shift stability of the ambient period incrementProved

    Oct 2026

  • Angle defect of a period cocycleProved

    Oct 2026

  • Radial transversality on the critical estimate regionDisproved

    Oct 2026

  • Regularity of the ambient and frame comparison pathsProved

    Oct 2026

  • Existence of the ambient determinant rotation angleProved

    Sep 2026

  • Period cocycle of the variational flowProved

    Sep 2026

  • Strict convexity at the critical parametersDisproved

    Sep 2026

  • Critical EH reference model lands in the estimate regionDisproved

    Sep 2026

  • Closed-orbit winding transfers along the transportDisproved

    Sep 2026

  • Robustness of ambient rotation under coefficient perturbationProved

    Sep 2026

  • Transverse winding transfers along the transportDisproved

    Sep 2026

  • Closed orbits transport to the regularization modelProved

    Sep 2026

  • Bounded defect of the ambient rotation under compositionProved

    Sep 2026

  • Positive momentum Hessian bounds ambient rotation lossProved

    Sep 2026

  • Interior maximum-principle step for resolvent positivityProved

    Sep 2026

  • Frobenius inner product of PSD matrices is nonnegativeProved

    Sep 2026

  • Hessian PSD at a local minimizer, localized to a neighborhoodProved

    Sep 2026

  • Hessian is positive-semidefinite at a local minimizerProved

    Sep 2026

  • Second-order necessary condition for a one-variable local minimumProved

    Sep 2026

  • Uniform density of Lipschitz maps on the closed regionProved

    Sep 2026

  • The standard Hopf circle bounds a positive elliptic rational diskProved

    Sep 2026

  • A sphere contact isotopy carries the standard Hopf circle through transverse embeddingsProved

    Sep 2026

  • Radial normalization scales the radial contact form by the inverse squared radiusProved

    Sep 2026

  • Complete clocks preserve prime periodic orbits and their geometric tracesProved

    Sep 2026

  • Complete Hamiltonian time change to a convex regularization modelProved

    Sep 2026

  • Smooth pullback of a rational page through complete regularization clocksProved

    Sep 2026

  • From root convergence to normalized log convergenceProved

    Sep 2026

  • Continuous extension of far-crossing coordinates at collisionProved

    Sep 2026

  • Strict horizontal monotonicity along a far shooting arcProved

    Sep 2026

  • Quotient page lifts to a cover-level rational pageProved

    Sep 2026

  • A lifted rational page descends through the antipodal coverProved

    Sep 2026

  • Positive determinant of THess\mathrm{THess}THess on the energy component implies positive definitenessProved

    Sep 2026

Posted 50

  • Diffeomorphism isotopy joining any equivariant contactomorphismOpen

    Oct 2026

  • Diffeomorphism isotopies upgrade to contact isotopiesOpen

    Oct 2026

  • Uniform strict convexity of the Levi-Civita surface on the low-energy tailProved

    Oct 2026

  • Equivariant sphere diffeomorphisms and diffeomorphism isotopiesDefinition

    Oct 2026

  • Uniform convex regularization model on the low-energy tailProved

    Oct 2026

  • Shift-invariance of anchored-periodic Hamiltonian solutionsProved

    Oct 2026

  • No short return after visiting the saddle-centersProved

    Oct 2026

  • No short subcritical periodic orbits near the saddle-centersProved

    Oct 2026

  • Slow escape segment near the subcritical saddle-centersProved

    Oct 2026

  • Convex body from a regular star-shaped level with positive HessianDisproved

    Oct 2026

  • Regularity, compactness and star-shapedness of the left EH componentProved

    Oct 2026

  • Positive tangential Hessian on the subcritical left EH componentProved

    Oct 2026

  • Subcritical left EH component bounds a compact convex bodyProved

    Oct 2026

  • Smooth equivariant isotopies upgrade to contact isotopiesOpen

    Oct 2026

  • Smooth equivariant isotopy to any equivariant contactomorphismOpen

    Oct 2026

  • Regularization models preserve the transverse Hopf classOpen

    Oct 2026

  • The Levi-Civita retrograde binding is a transverse Hopf fiberOpen

    Oct 2026

  • Local convex body and positive tangential Hessian in centered elliptic-hyperbolic coordinatesProved

    Oct 2026

  • Collision-compatible Levi-Civita to elliptic-hyperbolic coordinates near a fixed subcritical energyProved

    Oct 2026

  • Centered left elliptic-hyperbolic Hamiltonian and selected energy componentDefinition

    Oct 2026

  • Closed-orbit winding transfers along the transportDisproved

    Sep 2026

  • Persistence of strict convexity under perturbationOpen

    Sep 2026

  • Strict convexity at the critical parametersDisproved

    Sep 2026

  • Closed orbits transport to the regularization modelProved

    Sep 2026

  • Transverse winding transfers along the transportDisproved

    Sep 2026

  • Winding comparison for regular comparison pathsProved

    Sep 2026

  • Regularity of the ambient and frame comparison pathsProved

    Sep 2026

  • Angle defect of a period cocycleProved

    Sep 2026

  • Period cocycle of the variational flowProved

    Sep 2026

  • Linear ambient-angle growth from the spectral splittingProved

    Sep 2026

  • Spectral splitting of the saddle-center linearizationProved

    Sep 2026

  • Shift stability of the ambient period incrementProved

    Sep 2026

  • Ambient-to-frame comparison over one base periodProved

    Sep 2026

  • Robustness of ambient rotation under coefficient perturbationProved

    Sep 2026

  • Unbounded rotation of the saddle-center linearizationProved

    Sep 2026

  • Bounded defect of the ambient rotation under compositionProved

    Sep 2026

  • Ambient rotation controls transverse winding up to 4piProved

    Sep 2026

  • Existence of the ambient determinant rotation angleProved

    Sep 2026

  • Robust rotation growth for the saddle-center linear modelProved

    Sep 2026

  • Model rational page from an elliptic disk under dynamical convexityOpen

    Sep 2026

  • A transverse Hopf isotopy spans an elliptic diskOpen

    Sep 2026

  • Dynamical convexity of a convex regularization modelOpen

    Sep 2026

  • Strictly convex star-shaped points carry index at least threeOpen

    Sep 2026

  • Dynamical convexity pulls back along regularization modelsOpen

    Sep 2026

  • Strict convexity away from the saddle-centers in a regularization modelProved

    Sep 2026

  • Ambient determinant rotation controls periodic transverse windingProved

    Sep 2026

  • Regularization models and strictly convex star-shaped pointsDefinition

    Sep 2026

  • Arbitrarily large ambient rotation on a long saddle-center segmentProved

    Sep 2026

  • Positive momentum Hessian bounds ambient rotation lossProved

    Sep 2026

  • Ambient determinant rotation of Hamiltonian variational flowsDefinition

    Sep 2026

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